Can we really eliminate worksheets?

Thanks to Jo, I came across Woody and his post about eliminating worksheets. He says, among other things, that using worksheets:

1. Uses an unspeakable amount of paper. ...
2. Creates teachers that begin to rely on a 1-dimensional teaching method. Introduce... teach... have them fill in the blanks.
3. Creates dependent learners. ...
4. Creates a sense of monotony and boredom amongst most students....
5. Dilutes creativity. ...
6. Creates a stack of graded worksheets that is taken home and thrown away. ...

I am fighting a worksheet-driven curriculum at work. We use worksheets and test according to what is on the worksheets. I use worksheets -- but not fill-in-the-blank ones if I can help it. My students write sentences and paragraphs. They read stories. But they aren't always able to transfer that knowledge to the tests. I wonder if they wouldn't do better on the tests if I gave them more fill-in-the-blank worksheets.

That isn't to say that I am thinking of changing the way I teach to include more worksheets. But it does mean that I have to find a way to prepare students for the kind of testing that they will be forced to undergo. I have no say about the testing that is done; I am expected to use the same test everyone else does. So somehow I have to find a way for it to work for my students while not watering down the way I want to teach. I have been spending a lot of time thinking about this, and I don't know if I have reached a conclusion or not.